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Unformatted text preview: UFESI6314 DMORMidterm Cover page 1 of 1package page __ of __ESI 6314: Midterm Take Home Exam Due November 3rdName: Luther SetzerThere are five total questions.Pleaseremember that you are not allowed to communicate with anyoneregarding this exam except for the instructor or the TAs. Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 5447435UFESI6314 DMORMidterm Cover page 1 of 1package page __ of __Question 1 (15 points): True/False and why/why notThe following five questions are true/false. Credit is given onlyif a brief rationale is provided with your answers. (A sentence or two will suffice.) A simple "true" or "false" will not earn any points.Part a (3 points): Alloptimal solutions to a linear program exist at extreme points.Part b (3 points): In the simplex method for a minimization problem, the objective function strictly decreases at each iteration until an optimal solution is found. (An iteration consists of entering a nonbasic variable and exiting a basic variable.)Part c (3 points): The minimum ratio test is designed to ensure that no variable becomes negative in our solution (except maybe for the zvalue itself).Part d (3 points): If both a primal problem and its dual have feasible solutions, neither problem can be unbounded.Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 5447435UFESI6314 DMORMidterm Cover page 1 of 1package page __ of __Part e (3 points): Suppose that the shadow price for a constraint is equal to 5, and that its range allows an increase of 10 and a decrease of 3 before the basis changes. Then if the righthandside for that constraint is increased by 5, the optimal objective function value will increase by 25.Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 5447435UFESI6314 DMORMidterm Cover page 1 of 1package page __ of __Question 2 (20 points):Model the following problem as a linear program. Consider a cancer patient who is being treated with radiation therapy. The doctor has determined that she should receive treatment in a twodimensional crosssection, represented by a 6 x 6 grid (or matrix). The following matrix gives the number of units of radiation that should be received:912967108668786910109977119116511...
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 Fall '09
 VLADIMIRLBOGINSKI
 Linear Programming, Optimization, Simplex algorithm, Kennedy Space Center, Luther Setzer, package page __

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